EMA 3702L: MECHANICS AND MATERIALS SCIENCE LAB

PRINCIPAL STRESS AND STRAIN

Objectives

Use a rosette strain gage and digital strain indicator to measure the strains on the surface of a loaded cantilever beam, to determine the principal strains and stresses, the Poisson's ratio, and the angle of offset of the rosette to the principal axes.

Introduction

The strain on the surface of the cantilever beam is able to be measure by using a strain gage, however a 45^o rosette strain gage is used to determine three independent components of plane strain. The principal stresses, Poisson’s ratio and the angle of offset of the rosette to the principal axes can be calculated from those three strains (e_{1 ,} e₂ and e₃) by the following formulas:

Principal strains:

where: e_{1 ,} e₂ and e₃ are three strain values measured by the rosette

Poisson’s ratio:

where: e_p and e_q are principal strains.

Principal stresses:

,

where: s_p and s_q are principal stresses.

E is the modulus of elasticity.

The angle between gage axis and principal axis:

where: q_p and q_q are the angles between the rosette and two principal stress axes.

Procedures

Step 1: Measure the length, width and thickness of the beam and the distance from the point of loading to the rosette strain gage. Note the material of the beam.

Step 2: Calibration Digital Strain Indicator following the instruction on it.

Step 3: Place the unloaded weight hanger on the beam and adjust the zero setting for each of the strain gages.

Step 4: Increase the load and record the each gage strain data from the indicator.

Step 5: Repeat step 4 at least three more times.

Analysis and Discussion

Use the equation to calculate the principal strains, Poisson’s ratio, principal stresses for all tested data, and the angle of offset of the rosette strain gage to the principal axes. Use statistics method to determine the offset angles and calculate the standard deviation. Plot a chart of Poisson's ratio versus the load. Discuss the results.

Report Requirement

A short version report must be submitted both printed and electronic copies on the due date (see the announcement board).